Final answer:
To find the fifth term of (x^2+y^2)^13, we can use the binomial theorem. The fifth term is given by C(13, 4) * x^18 * y^8.
Step-by-step explanation:
To find the fifth term of (x^2+y^2)^13, we can use the binomial theorem. The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n can be found using the formula:
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n
In this case, a = x^2 and b = y^2, and we want to find the fifth term, so n = 13 and the term number is k = 5.
Plugging in the values, the fifth term is given by:
C(13, 4) * (x^2)^(13-4) * (y^2)^4
Let's simplify this further:
C(13, 4) * x^18 * y^8